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Gravitational Potential Energy: Understanding the Science of Heights
What Is Gravitational Potential Energy?
Gravitational potential energy (\( GPE \)) is the energy stored in an object due to its height in a gravitational field:
\[ GPE = mgh \]
Where:
- \( m \): Mass (kg)
- \( g \): Gravitational acceleration (\( 9.8 \, \text{m/s}^2 \))
- \( h \): Height above a reference point (m)
Key Principles of GPE
Energy Conservation
GPE converts to kinetic energy as an object falls:
\[ mgh = \frac{1}{2}mv^2 \]
Work Done Against Gravity
Work is required to lift an object, equal to the increase in \( GPE \).
Applications of GPE
Hydropower
Water stored at height in dams is released to generate electricity.
Engineering
Elevators and cranes rely on calculations involving \( GPE \).
Space Science
Escape velocity depends on the gravitational potential energy of a planet.
Example Problem
A \( 10 \, \text{kg} \) object is lifted \( 5 \, \text{m} \). Calculate its gravitational potential energy.
- Formula:
\[ GPE = mgh \] - Substitute Values:
\[ GPE = 10 \times 9.8 \times 5 = 490 \, \text{J} \]
Common Mistakes in GPE Calculations
- Using incorrect units for mass or height
- Ignoring energy losses due to friction or air resistance
- Mixing up GPE and elastic potential energy
Practice Questions
- A \( 20 \, \text{kg} \) object is raised \( 10 \, \text{m} \). Calculate the \( GPE \).
- Explain how GPE is used in hydropower systems.
- Describe one application of GPE in space exploration.